Is it obligatory to repeat the prayers that were performed after the emission of wind without sound or smell, based on a mistaken belief that this does not nullify ablution, especially if the act occurred before puberty?

The emission of wind (flatulence) invalidates ablution, even if it's without sound or odor. However, if you are not certain that your ablution has been invalidated by it, then you are not required to repeat it, because certainty is not removed by doubt, and the certainty of ablution is not lifted except by a verified invalidator. Also, missed prayers from before puberty do not need to be made up.